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66 Cards in this Set
- Front
- Back
The science that deals with the collection, classification, summarizing, organizing, analyzing and interpreting of numerical information
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statistics
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three areas of statistics
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descriptive, statistical, prediction and regression
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all of the items of interest in a given problem
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population
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finite subset drawn from the population
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sample
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characteristic or property of interest
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variable
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making a statement about a characteristic of the overall true population based on a characteristic from a random sample drawn from the population
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statistical inference
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can be described numerically; age, weight, height, size of family, monthly sales
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quantitative data
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categorical data; color of eyes, employment status, defect or no defect
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qualitative data
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difference between the estimator and the true population parameter; sampling info vs population info
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sampling error
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all other errors that cause a difference btw estimator and population parameter
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nonsampling error
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where every subset of fixed size in the population has equal probability of being included
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random sample
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a variable that contains the outcomes of a chance experiment
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random variable
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r.v. can take finite number of values (countable);think of as “separated values”
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discrete random variable
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r.v. can take any value in intervals (measurements);always infinite
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continuous random variable
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# of defectives in a lot of size 50, type of customer complaints
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discrete random variable
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wait time, response time of a computer system
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continuous random variable
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Each probability p(x) must be between 0 and 1 inclusive
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probability distribution requirements
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can only take on two values;
yes/no, pass/fail, etc.; n identical trials in the experiment; trials are independent |
binomial random variables; characteristics of...
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probability of success
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p
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probability of failure
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q
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relationship between p and q
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p + q = 1
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Relative frequency notion of probability
Binomial formula Binomial table Normal approximation to the binomial |
4 methods for calculating binomial probabilities
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It gives us the combination count, or the number of samples that produces exactly x successes in n trials
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Binomial coefficient
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4 things to describe descriptive statistics
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location, dispersion, shape, data patters
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measures of central tendency
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location
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measures of variability
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dispersion
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measures of central tendency
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mean, median, mode
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measures of variability
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standard deviation, variance, range, interquartile range
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shape
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skew
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most frequently occurring observation in a distribution
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mode
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middlemost observation in an ordered array
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median
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sum of all the values divided by the number of values (sample size or population size)
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mean
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[max minus min]
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range
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measures of location that divide a group of data into four subgroups; lower quartile, middle quartile, upper quartile; Q(u)-Q(l); Range of the middle 50% of the distribution
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Interquartile range
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25%
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lower quartile
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50%
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middle quartile
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75%
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upper quartile
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Tells how far on average each value is away from the mean; notation: population / sample
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variance
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notation: population / sample
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standard deviation
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Standardized scores; Numerical value reflects the standing of a measurement relative to the mean; Tells how far away from the mean the value is in terms of standard deviations; Algebraic sign (+ or -) indicates whether the measurement is larger or smaller relative to the mean
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z-score
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data points that do not follow the general pattern of data
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outliers
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extreme values of the observed data
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whiskers
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Based on the sample evidence; making a statement about the population
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statistical inference
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Based on known populations; making a statement about the probability of an event
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probability
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act or process of observation that leads to a single outcome that cannot be predicted with certainty
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experiment
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the most basic outcome of an experiment
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sample point
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all of the sample points of an experiment
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sample space
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specific collection of sample points
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event
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probability rules for sample points
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1) individual probabilities must lie between 0 and 1 (inclusive)
2) the sum of probabilities of all sample points in a sample space must equal 1 |
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# of sample points that correspond to an event relative to the total # of sample points in the sample space
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probability
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the event that A does not occur
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complement of event A
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if either A or B or both occurs
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union
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if both A and B simultaneously occur
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intersection
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if A and B have no sample space outcomes in common {AunionB contains no sample points}
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mutually exclusive events
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We have information – prior knowledge – that affects the probability of an event
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conditional probability
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if the occurrence of one does not alter the probability of the other
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independent events
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may take on any value in an interval
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continuous rv
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Make a statement about the overall true population parameters
Based on information from a random sample |
statistical inference
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Tells how far, on average the sample statistic is away from the population parameter; SE
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st. dev. of sampling distribution
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Mean of the sampling distribution of the statistic X-Bar equals the mean of the population; Standard deviation of the sampling distribution of the statistic X-Bar equals the standard deviation of the population divided by the square root of the sample size n
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central limit theorem
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Provides a single value
Based on observations from 1 sample Gives no information about how close the point estimator is to the unknown population parameter |
point estimate
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Provides a range of values
Based on observations from 1 sample Gives information about closeness to unknown population parameter Stated in terms of probability To know exact closeness requires knowing population parameter that is usually unknown |
interval estimate
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the measure of the precision of the estimate
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margin for error
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Involve qualitative variables
Fraction or % of population in a category If two qualitative outcomes, binomial distribution |
Proportion
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observed level of significance
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p-value
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probability of obtaining a test statistic more extreme (or than actual observed value given H0 is true
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p-value
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